In my experience, plants love a certain amount of [URL="http://store.rockdustlocal.com/Sea-Minerals-20-lbs_p_25.html"]sea salt[/URL], but if they get too much too often, it can kill them. Anyway, the right amount really perks them up and makes them greener. However, if you're growing watermelons, it can make the rind salty. I did have one watermelon with a very unusually sweet rind, however.

Blacktail Mountain had a salty rind on one fruit, and a second year Ledmon had a very sweet rind on one fruit (the largest, and most unique fruit in the patch). At least one other variety had a salty rind, but the other watermelons were normal with regard to rind flavor. Yes, I eat watermelon rinds. They make a great condiment if you peel the skin off the rinds with a carrot peeler and chop the rinds up into small bits with something like a food chopper or processor. Peeling the skin is just to make them easier to chop up (it's perfectly edible).

Sea minerals also seem to help plants against fungal infections and pests to some degree.

My sea minerals were kind of oily. I'm not sure why or if that's natural.

I did have an exceedingly sweet watermelon (I used sea minerals on it). I didn't notice much about tomatoes I had used sea minerals on, with regard to flavor (but I didn't use it on many varieties). I did use it on Pineapple, for sure, but it wasn't true to type (it was all yellow).

It should be noted that blood is said to have the same mineral composition as seawater. People use blood meal in their gardens. I imagine it has a high sodium content.

A lot of our natural fertilizers here come from the sea so I guess are naturally a bit salty. Kelp for sure makes vegetables sweeter, but it's rich in potassium too, and that is known to affect sweetness in tomatoes.
The only thing I ever heard sea water was used for in farming here, is to get the cabbage to form heads they would splash sea water on them.8-)

Salt can be toxic, depends on the plant, tomato is not particularly sensitive, beans are.
Salt has another effect, it increases the osmotic pressure making water uptake more difficult for the roots, like they are dryer than they really are. So the moisture availabilty of salted earth even when wet is more like they are being dry farmed, which produces fewer or smaller sweeter tomatoes.

I can wilt my hydroponic tomatoes while the roots are wet with a very strong hydroponic solution, or by adding salt.
The roots can't get the water into them. Tomato tastes great, but production suffers quite a bit.

My conclusion is, its not worth adding salt, I just run a stronger solution later in the season.

I think the secret to sweet tomatoes is plenty of sunlight, and the secret to sweet [URL="http://www.rareseeds.com/litchi-tomato-or-morelle-de-balbis/"]Morelle De Balbis[/URL] is prolonged cold weather; the secret to sweet tomatillos seems to be to let them ripen all the way (i.e. fall off the plant; one of the sweetest ones I ever had ripened in the shade). The secret to sweet muskmelons seems to be the same as the secret to sweet tomatoes.